I find-out a module to calculate the reduced row form.
http://perso.univ-rennes1.fr/antoine.chambert-loir/2006-07/a6/maxima.html
I tested it, it looks fine. This is the result for my exemple:
(%i15) load(rref);
(%o15) /usr/share/maxima/5.10.0/share/matrix/rref.mac
(%i16) rref(%o11);
(%o16) matrix([1,0,1,0,1],[0,1,-2,0,3],[0,0,0,1,-5],[0,0,0,0,0])
and it's ok!
Thank you for your help!
Patrick